Transitioning to the Common Core State Standards – Mathematics 4 th Grade Session 3 Pam Hutchison

Transitioning to the Common Core State

Standards – Mathematics

4th Grade Session 3Pam Hutchison

[email protected]

AGENDA Multi-Step and Other Word Problems Review Math Practice Standards Fractions and Decimals Lines, Line Segments, Angles and Rays

What’s an Angle Classifying Angles Measuring Angles

Data and Line Plots

Multi-Step Word Problems

A pair of hippos weighed 5,201 kg together. The female weighed 2,038 kg. How much more did the male weigh than the female?


A copper wire was 240 m long. After 60 m was cut off, it was double the length of a steel wire. How much longer was the copper wire than the steel wire at first?


Jennifer has 256 pink beads. Stella has 3 times as many beads as Jennifer. Tiah has 104 more beads than Stella. How many beads does Tiah have?


Sandy’s garden has 42 plants in each row. She has 2 rows of yellow corn and 20 rows of white corn. How many plants does she have?

CCSS Mathematical Practices

REASONING AND EXPLAINING2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of others

MODELING AND USING TOOLS4. Model with mathematics5. Use appropriate tools strategically

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SEEING STRUCTURE AND GENERALIZING7. Look for and make use of structure8. Look for and express regularity in repeated reasoning

Math Practice StandardsUsing the MP descriptions from the 4th Grade Flipbook, describe how you are developing each of these practices in your students. Be ready to share an example for each

of the 8 Math Practices Standards. Which standard is the hardest to

implement?

4.NF.5Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.)

4.NF.5 Focus on working with grids, number

lines and other models (not algorithms) Base ten blocks and other place value

models can be used to explore the relationship between fractions with denominators of 10 and denominators of 100

This work lays the foundation for decimal operations in fifth grade.

3 tenths = 30 hundredths

0.3 = 0.30=

103

10030

10060

106

5 tenths + 7 hundredths =57 hundredths

1002

104

1002

104

10042

1002

10040

10042

4.NF.6Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

4.NF.6 Focus on connections between

fractions with denominators of 10 and 100 and the place value chart.

Connect tenths and hundredths to place value chart

Connect to 0.32 to1002

103

10032

4.NF.6 Students connect with 0.32 and

represent it on a place value model.10032

4.NF.7Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Planning a LessonConnecting fractions, decimals, and place value. Review

Name the fractionsTenths gridHundredths gridNumber line – tenths and hundredths

Write in expanded form

Planning a Lesson

Word Problem: In the school chorus, of the students are girls. If there are 10 boys in the chorus, how many girls are there?

53

Place Value Hundreds Tens Ones

Place Value Ones Tenths

Decimal Place Value Ones Tenths

Decimal Place Value Ones Tenths Hundredths

Fractions and Decimals So we can name some fractions as

decimals

How do we know which fractions we can also name as decimals?

Fractions and Decimals How do we know which fractions we

can also name as decimals?

When the denominator is a place value number (also called a power of 10)

Fractions and Decimals For example:

can also be written as 0.3

can also be written as 0.72

What about ?

103

10072

1008

Classwork See Fractions and Decimals worksheet

Engage NY Fluency Practice

Designed to promote automaticity of key concepts

Daily Math is another form of fluency practice

Application Problem Designed to help students understand how

to choose and apply the correct mathematics concept to solve real world problems

Read-Draw-Write (RDW): Read the problem, draw and label, write a number sentence, and write a word sentence

Engage NY Concept Development

Major portion of instruction Deliberate progression of material, from

concrete to pictorial to abstract Student Debrief

Students analyze the learning that occurred

Help them make connections between parts of the lesson, concepts, strategies, and tools on their own

Engage NYModule 5 Lesson 28 MD.4 Make a line plot to display a data

set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Engage NYModule 4: Angle Measures and Plane Figures Topic A: Lines and Angles Topic B: Angle Measurement Topic C: Problem Solving with Angle

Measurement Topic D: Two-Dimensional Figures and

Symmetry

Topic A – p A.2

4.G.1

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Lesson 1Identify and draw points, lines, line segments, rays, and angles and recognize them in various contexts and familiar figures. Concept Development p A.4 (bottom)

Problem 1: Draw, identify, and label points, a line segment, and a line.

Problem 2: Draw, identify, and label rays and angles.

Problem 3: Draw, identify, and label points, line segments, and angles in a familiar figure.

Problem 4: Analyze of a familiar figure.

Lesson 1 Problem Set A.11-12

Student Debrief Questions A.9-10 Exit Ticket A.13

Homework A.14-15

Lesson 2Use right angles to determine whether angles are equal to, greater than, or less than right angles. Draw right, obtuse, and acute angles. Fluency Practice p A.17

Identify Two-Dimensional Figures Physiometry

Application Problem – Line Segments

Lesson 2Conceptual Development p A. 18 Problem 1: Creating right angles

through paper folding activity. Problem 2: Determine whether angles

are equal to, greater than, or less than a right angle. Practice Sheet p A.24

Problem 3: Draw right, acute, and obtuse angles.



Homework A.29-31

Lesson 3Identify, define, and draw perpendicular lines. Fluency Practice p A.32


Application Problem – Line Segments (A.34)

Lesson 3Conceptual Development p A.35 Problem 1: Define perpendicular lines. Problem 2: Identify perpendicular lines

by measuring right angles with a right angle template.

Problem 3: Recognize and write symbols for perpendicular segments.

Problem 4: Draw perpendicular line segments.



Homework A.43-35

Lesson 4Identify, define, and draw parallel lines. Fluency Practice p A.46


Application Problem - reviews perpendicular and intersecting lines (A.48)

Lesson 4Conceptual Development p A.49 Problem 1: Define and

identify parallel lines. Problem 2: Identify

parallel lines using a right angle template.

Lesson 4Conceptual Development Problem 3: Represent

parallel lines with symbols.

Problem 4: Draw parallel lines.



Homework A.58-60

Topic B – p B.2

4.MD.5Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a) An angle is measured with reference to a

circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

b) An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

4.MD.6

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Lesson 5Use a circular protractor to understand a 1-degree angle as 1/360 of a turn. Explore benchmark angles using the protractor. Fluency Practice p B.2


Application Problem – right angles (B.5)

Lesson 5Conceptual Development p B.5 Directions for Constructing a Paper

Protractor:

Lesson 5Conceptual Development p B.5 Problem 1: Reason

about the number of turns necessary to make a full turn with different fractions of a full turn.

Lesson 5 Problem 2: Use a circular protractor to

determine that a quarter-turn or a right angle measures 90 degrees, a half turn measures 180 degrees, a three quarter-turn measures 270 degrees, and a full rotation measures 360 degrees.

Lesson 5 Problem 3: Measure and draw

benchmark angles with the protractor.

Lesson 6Use varied protractors to distinguish angle measure from length measurement. Fluency Practice p B.

Application Problem – (B.)

Conceptual Development p B.

Lesson 7Measure and draw angles. Sketch given angle measures and verify with a protractor. Fluency Practice p B.



Lesson 8Identify and measure angles as turns and recognize them in various contexts. Fluency Practice p B.



Transitioning to the Common Core State Standards – Mathematics 4 th Grade Session 3 Pam Hutchison

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